Final answer to the problem
$3y+2x$
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Step-by-step Solution
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1
The trinomial $4x^2+12yx+9y^2$ is a perfect square trinomial, because it's discriminant is equal to zero
$\Delta=b^2-4ac=12^2-4\left(4\right)\left(9\right) = 0$
2
Using the perfect square trinomial formula
$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{4x^2}\:and\:b=\sqrt{9y^2}$
3
Factoring the perfect square trinomial
$\frac{\left(2x+3y\right)^{2}}{3y+2x}$
4
Simplify the fraction $\frac{\left(2x+3y\right)^{2}}{3y+2x}$ by $3y+2x$
$3y+2x$
Final answer to the problem
$3y+2x$